Convergence of ADMM for multi-block nonconvex separable optimization models

Guo, Ke; Han, Deren; Wang, David Z.W.; Wu, Tingting

doi:10.1007/s11464-017-0631-6

Cited by 41 publications

(24 citation statements)

References 26 publications

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“…where the second equality follows from the definition of in (27), and the second inequality comes from (29) and (33). Then, assertion (52) is thus proved.…”

Section: Lemma 10mentioning

confidence: 73%

“…We compare it with the splitting method for separable convex programming (denoted by HTY) in [30], the full Jacobian decomposition of the augmented Lagrangian method (denoted by FJDALM) in [13], and the fully parallel ADMM (denoted by PADMM) in [14]. Through these numerical experiments, we want to illustrate that (1) suitable proximal terms can enhance PFPSM's numerical efficiency in practice, (2) larger values of the Glowinski relaxation factor can often accelerate PFPSM's convergence speed, and (3) compared with the other three ADMM-type methods the dynamically updated step size defined in (27) can accelerate the convergence of PFPSM. All codes were written by Matlab R2010a and conducted on a ThinkPad notebook with Pentium(R) Dual-Core CPU T4400@2.2 GHz, 4 GB of memory.…”

Section: Numerical Resultsmentioning

confidence: 99%

“…Therefore, we can maximize Φ ( ) to accelerate the convergence of PFPSM. Note that Φ ( ) is a quadratic function of and it reaches its maximum at defined by (27). The following theorem shows that the sequence { } generated by PFPSM is Fejér monotone with respect to the solution set W * of VI(W, , ).…”

Section: Lemma 10mentioning

confidence: 99%

“…For some very large-scale (6), computing the step size defined by (27) is a fussy work needing much calculating. For these instances, set = in PFPSM, and the step size can be fixed as the constant 0 defined in Lemma 6.…”

Section: Remark 12mentioning

confidence: 99%

“…There are three strategies to deal with the issue: (1) the substitution procedure [13,21]; (2) the technique of regularization [14,22]; (3) the technique of small step size [23]. For other recent developments of ADMM, including the (sub)linear convergence rate, various acceleration techniques, indefinite regularized matrices, larger step size, and its generalization to solve nonconvex and nonsmooth multiblock separable programming, we refer to [24][25][26][27][28].…”

Section: Introductionmentioning

confidence: 99%

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A Proximal Fully Parallel Splitting Method for Stable Principal Component Pursuit

Sun

Liu

Sun

2017

Mathematical Problems in Engineering

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As a special three-block separable convex programming, the stable principal component pursuit (SPCP) arises in many different disciplines, such as statistical learning, signal processing, and web data ranking. In this paper, we propose a proximal fully parallel splitting method (PFPSM) for solving SPCP, in which the resulting subproblems all admit closed-form solutions and can be solved in distributed manners. Compared with other similar algorithms in the literature, PFPSM attaches a Glowinski relaxation factor ∈ ( √ 3/2, 2/ √ 3) to the updating formula for its Lagrange multiplier, which can be used to accelerate the convergence of the generated sequence. Under mild conditions, the global convergence of PFPSM is proved. Preliminary computational results show that the proposed algorithm works very well in practice.

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“…where the second equality follows from the definition of in (27), and the second inequality comes from (29) and (33). Then, assertion (52) is thus proved.…”

Section: Lemma 10mentioning

confidence: 73%